TY - JOUR
T1 - A rational map with infinitely many points of distinct arithmetic degrees
AU - Lesieutre, John
AU - Satriano, Matthew
N1 - Funding Information:
Acknowledgements. We are grateful to Joseph Silverman for useful comments. J.L. is partially supported by NSF grant DMS-1700898. M.S. is partially supported by NSERC grant RGPIN-2015-05631.
Publisher Copyright:
© Cambridge University Press, 2019.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - Let be a dominant rational self-map of a smooth projective variety defined over. For each point whose forward -orbit is well defined, Silverman introduced the arithmetic degree, which measures the growth rate of the heights of the points. Kawaguchi and Silverman conjectured that is well defined and that, as varies, the set of values obtained by is finite. Based on constructions by Bedford and Kim and by McMullen, we give a counterexample to this conjecture when.
AB - Let be a dominant rational self-map of a smooth projective variety defined over. For each point whose forward -orbit is well defined, Silverman introduced the arithmetic degree, which measures the growth rate of the heights of the points. Kawaguchi and Silverman conjectured that is well defined and that, as varies, the set of values obtained by is finite. Based on constructions by Bedford and Kim and by McMullen, we give a counterexample to this conjecture when.
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U2 - 10.1017/etds.2019.30
DO - 10.1017/etds.2019.30
M3 - Article
AN - SCOPUS:85065258676
SN - 0143-3857
VL - 40
SP - 3051
EP - 3055
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 11
ER -